1. Field of the Invention
The present invention relates to methods of stabilizing spectra in spectrometry and more particularly methods of stabilizing measurements by reducing in numerical computation the fluctuations of the spectral baseline due to changes in temperature, source voltage, and the like within the spectroscope and the fluctuations of transmittance due to changes in the incidence angle of the light applied to the measured object.
2. Description of the Related Art
In general, quantitative analysis for the concentration of a specified component can use an analytical curve obtained beforehand by measuring the energy spectrum of light transmitted through or alternatively reflected by a sample whose concentration is already known. As methods of obtaining the analytical curve, generally known are a method in which a single wavelength is used and a method in which two or more wavelengths are used.
However, fluctuations of the spectral baseline occur in the spectrum caused by changes in temperature inside and outside the spectroscope, changes in the voltage of the power supply, and the like. These fluctuations of the baseline reduce the accuracy of the quantitative analysis, so that it is necessary to eliminate the error components in the spectrum.
As methods of reducing the baseline fluctuations by numerical computation, double-wavelength baseline compensation, digital differentiation, and the low-frequency filtering Fourier transform are generally known. Each of these methods is briefly described in the following.
DOUBLE-WAVELENGTH BASELINE COMPENSATION.
The method of double-wavelength baseline compensation uses two wavelengths .lambda..sub.1 and .lambda..sub.2 at which the absorbances are constant for any solution composition to cancel the baseline component out. Specifically, the two wavelengths .lambda..sub.1 and .lambda..sub.2 respectively satisfy the following equations (1) and (2). ##EQU1## where .alpha..sub.i,.lambda..sub.1 : absorptivity at wavelength .lambda..sub.1,
c.sub.i : concentration of component i, PA1 n: the number of components in the solution, PA1 l: cell length. ##EQU2## where .alpha..sub.i,.lambda..sub.2 : absorptivity at wavelength .lambda..sub.2, PA1 c.sub.i : concentration of component i, PA1 n: the number of components in the solution, PA1 l: cell length. PA1 I(.lambda., t): intensity of transmitted light at wavelength .lambda. and time t, PA1 I(.lambda..sub.r, t): intensity of transmitted light at wavelength .lambda..sub.r and time t, PA1 I.sub.0 (.lambda., t.sub.0): intensity of incident light at wavelength .lambda. and time t.sub.0, PA1 I.sub.0 (.lambda..sub.r, t.sub.0): intensity of incident light at wavelength .lambda..sub.r and time t.sub.0, PA1 p(.lambda., .theta.): surface transmittance of light incident at angle .theta. at wavelength .lambda., PA1 p(.lambda..sub.r, .theta.): surface transmittance of light incident at angle .theta. at wavelength .lambda..sub.r, PA1 .alpha..sub.i (.lambda.): absorption coefficient of component i at wavelength .lambda., PA1 .alpha..sub.i (.lambda..sub.r): absorption coefficient of component i at wavelength .lambda..sub.r, PA1 .theta.: incidence angle of light with the surface of the measured object PA1 c.sub.i : concentration of component i, and PA1 l: effective path length. PA1 p(.lambda.,.theta..sub.i).sub..parallel. : surface transmittance of light at wavelength .lambda. when horizontally polarized light is incident on the measured object at the incidence angle .theta..sub.i, PA1 p(.lambda., .theta.).sub..perp. : surface transmittance of light at wavelength .lambda. when vertically polarized light is incident on the measured object at the incidence angle .theta..sub.i, PA1 p(.lambda..sub.r, .theta.).sub..parallel. : surface transmittance of light at wavelength .lambda..sub.r when horizontally polarized light is incident on the measured object at the incidence angle .theta..sub.i, PA1 p(.lambda..sub.r, .theta.).sub..perp. : surface transmittance of light at wavelength .lambda..sub.r when vertically polarized light is incident on the measured object at the incidence angle .theta..sub.i, PA1 n.sub.1,.lambda. : index of refraction of medium 1 at wavelength .lambda., PA1 n.sub.2,.lambda. : index of refraction of medium 2 at wavelength .lambda., PA1 n.sub.1,.lambda..sbsb.r : index of refraction of medium 1 at wavelength .lambda..sub.r, PA1 n.sub.2,.lambda..sbsb.r : index of refraction of medium 2 at wavelength .lambda..sub.r : PA1 .theta..sub.i : incidence angle with the surface of measured object, and PA1 .theta..sub.t : refraction angle with the surface of measured object.
Therefore, if the absorbances of a measured absorption spectrum f(.lambda.) at wavelengths .lambda..sub.1 and .lambda..sub.2 are respectively const3 and const4, then the compensated spectrum is obtained by subtracting (const4-const3)/(.lambda..sub.2 -.lambda..sub.1).times.(.lambda.-.lambda..sub.1)+const3 from f(.lambda.).
DIGITAL DIFFERENTIATION
The digital differentiation method reduces or eliminates a drift at a low frequency by digitally differentiating absorbance with respect to a wavelength. The order of differentiation is generally first or second. The constant component independent of wavelength can be eliminated by the first order differentiation. The first-order drift with respect to the wavelength can be eliminated by the second order differentiation. In digital differentiation, absorbance is differentiated with respect to the wavelength, so that differentiation higher than the second order greatly distorts the signal. Therefore, the digital differentiation of the order higher than third is rarely used.
LOW-FREQUENCY FILTERING FOURIER TRANSFORM
The method of the low-frequency filtering Fourier transform that Fourier transforms the spectrum, i.e., converts the energy spectrum from the time domain to the frequency domain, to filter out the low-frequency components that are the causes of the baseline shift.
The method of double-wavelength compensation requires the two wavelengths .lambda..sub.1 and .lambda..sub.2 used for compensation to respectively satisfy the above equations (1) and (2). However, in multi-component solutions of more than two components, there often do not exist the two wavelengths that satisfy the above equations (1) and (2). In these cases the method of double-wavelength compensation cannot be used.
The method of digital differentiation enlarges high-frequency noise such as random noise by digital differentiation. Therefore, the bandwidth of the baseline fluctuations has to be wider than the bandwidth of the light absorbed by substances. Further, the derivative spectra are distorted by digital differentiation.
In the method of the low-frequency filtering Fourier transform, there is a problem that the information about light absorption by substances in a low-frequency domain is lost by filtering together with baseline fluctuation components.
Further, there is a problem common to digital differentiation and the low-frequency filtering Fourier transform. That is, if the energy E is a function of two variables, time t and wavelength .lambda., then the total differential of E(.lambda., t) is expressed by the following equation (3). EQU dE=(.differential.E/.differential..lambda.).sub.t d.lambda.+(.differential.E/.differential.t).sub..lambda. dt.(3)
The prior methods of digital differentiation and the low-frequency filtering Fourier transform are both operations on wavelength .lambda.. Therefore, the second term (.differential.E/.differential.t).sub..lambda. of the equation (3), which is a function of t, can not be reduced or eliminated.